Random features for high-dimensional nonlocal mean-field games

We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. avoid costly space-discretizations terms in state-space by passing to feature-space. This allows a seamless extension virtually any single-agent trajectory optimization algorithm. Here, we extend direct transcription optimal control setting. demonstrate efficiency our method solving MFG problems spaces which were previously out reach conventional non-deep-learning techniques.